A central point of our investigation is to compare to previous results given in Ref. [1]}, which have
been presented based on a 5PN EOB Hamiltonian. For the local parts of both Hamiltonians one may either perform a canonical
transformation, as done in Ref. [2]}, or determine the EOB potentials by an observable.
We will choose the latter way and use the local contribution to periastron advance \(K^{\rm loc,h}(\hat{E},j)\) .
Corresponding consistency checks can be performed by additional observables, such as the binding energy and periastron
advance for circular motion and also the expansion coefficients of the scattering angle.
